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Biometrika 1978 65(3):553-559; doi:10.1093/biomet/65.3.553
© 1978 by Biometrika Trust
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Optimal design measures with singular information matrices

S. D. SILVEY

Department of Statistics, University of Glasgow

The problem of establishing a useful necessary and sufficient condition for a design measure with singular information matrix to be Ds-optimal is well known. In this paper a sufficient condition involving a certain type of g-inverse is established for a more general convex criterion function to be minimized by such a design measure. The condition is necessary for DA-optimality and for a linear criterion function. There is some discussion about its necessity in general.

Key Words: Directional derivative • Generalized inverse • Optimal design measure • Singular information matrix • Theory of games


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